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A curvilinear extension of Iversen-Tsuji's theorem for simply connected domain


Author: Un Haing Choi
Journal: Proc. Amer. Math. Soc. 64 (1977), 47-51
MSC: Primary 30A72
DOI: https://doi.org/10.1090/S0002-9939-1977-0447576-3
MathSciNet review: 0447576
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Abstract: Let D be a simply connected domain with at least two boundary points in the complex plane, and t a boundary point of D. For a meromorphic function $ f(z)$ in D, $ \lim \sup \vert f(z)\vert{\text{as}}\;z \to t$ is given in terms of accessible boundary points and prime ends. This gives a curvilinear extension of Iversen-Tsuji's Theorem for a simply connected domain.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0447576-3
Keywords: Capacity, conformal null set, prime end, accessible boundary point, Perron process, Poisson integral, ambiguous point, $ \tfrac{1}{2}$-dimensional Hausdorff measure
Article copyright: © Copyright 1977 American Mathematical Society